Recently, array-compressed parallel transmission (acpTx) has been proposed as a low-cost solution to optimally drive a large number of transmit coils using a small number of transmit channels [1,2]. Figure 1 shows the proposed embodiment of acpTx [2], in which each transmit channel’s pulse is split across multiple transmit coils, and each coil receives the attenuated and phase shifted pulse. Compared to more general ones, this configuration has significant hardware simplicity with little penalty in pulse performance [1] . However, how to optimally assign coils to channels remains a question. Here we present an algorithm to jointly optimize coil-channel assignments along with acpTx pulse design, and to prune unnecessary coils. The method is validated and applied to simultaneous multislice and 3D-reduced FOV excitations, where the compressed many-coil arrays can outperform conventional arrays with the same number of input channels.The proposed acpTx pulse design with optimized coil-channel assignments is formulated as: $$\textrm{minimize } \phi(B); \textrm{s.t. rank}(B(\Theta_i)) = 1 (i = 1,...,N_{chan}) \textrm{ (Eqn 1)}$$ where $$$\phi$$$ is the pulse design cost function, $$$B$$$ the $$$N_t$$$ by $$$N_{coils}$$$ RF pulse matrix where $$$N_t$$$ is the number of pulse time points, $$$\Theta_i$$$ the coil-channel assignment vectors (1 vector for each input channel) that map the $$$N_{coils}$$$ transmit coils to the $$$N_{chan}$$$ input transmit channels. The problem is solved iteratively with following procedure: Step 1: The $$$B$$$ matrix is updated using a conventional parallel pulse design algorithm. Step 2: Soft thresholding is applied to the $$$B$$$ matrix to minimize its $$$L1$$$ norm. [3]. Step 3: Coil-channel assignments are made by calculating and sorting the $$$L2$$$ norm of each column of $$$B$$$, and assigning every other coil in the sorted list to the next channel. This assignment strategy ensures that the compressed array’s degrees of freedom are spent on the most important coil elements. Step 4: SVD truncation is applied to reduce the rank of each matrix $$$B(\Theta_i)$$$ to 1. This process is repeated until the cost function stops decreasing, yielding the pulse waveforms, the array compression weights, and the coil-channel assignments. Unnecessary coils can be optionally pruned according to the amplitudes of their array compression weights.To validate whether the proposed algorithm yields the best possible coil combinations, pulse designs were performed using simulated $$$B_1^+$$$ maps from a 7T 8 coil head transmit array [4]. AcpTx Pulses with $$$N_{chan} = 2$$$ were designed for the array using the proposed algorithm and compared to pulses designed using all other possible 8 coil-to-2 channel assignments. Three pTx pulse types were designed: (1) Reduced FOV spiral excitations with R = 3.6 acceleration [5], (2) Slice-specific multiband RF shims [6], and (3) Small-tip-angle $$$k_T$$$ points excitations [7]. The algorithm was then used to optimally compress large transmit coil arrays for two applications, and the performance of the compressed arrays was compared to application-specific arrays for which $$$N_{chan} = N_{coils}$$$. The first application was slice-specific multiband RF shimming, with an initial 24-loop array (Fig. 2b) compressed to 8 channels. The acpTx shims were compared to shims designed for the multiband-specific 8-coil array in [8] (Fig. 2a). The second application was selective excitation of the human occipital lobe with a 3D SPINS pulse [9], with an initial 36-loop array (Fig. 2d, with and without pruning down to 8 coils) compressed to 2 channels. The acpTx pulses were compared to pulses designed for a standard 2-coil array (Fig. 2c).Figure 3 shows that the proposed algorithm identifies the coil assignments with the lowest or near-lowest cost in all the pulse design scenarios, and that these combinations have significantly lower cost than previously-proposed sequential or interleaved coil assignments [1]. In both the multiband and occipital lobe imaging applications, the compressed coil arrays and pulses achieved lower NRMSE, lower total deposited RF power, and lower maximum 10g SAR (Figs. 4 and 5a,b) than the conventional coils. In the occipital excitation case, the algorithm pruned the original 36-coil array down to 8-coils while still maintaining better performance than the 2-coil array. Figure 5c shows that the coils remaining after pruning were at the back of the head, as would be expected.This study demonstrated an acpTx pulse design algorithm with optimal coil-to-channel assignments, which enables acpTx with reduced hardware sophistication. It was further shown in the occipital lobe excitation that the algorithm can identify the most important coil elements from a large set of candidate coils, and that the resulting arrays can outperform conventional arrays with the same number of input channels. This may have significant implications for pTx array design and optimization.